"I am just thrilled," she said in a telephone interview late Tuesday night, vowing to launch her general-election campaign Wednesday morning.
"We continue to spread our message that the attorney general's office needs to be manned - or womanned - by a prosecutor and not a politician," Kane said.
Kane, a former Lackawanna County prosecutor running her first campaign for elective office, defeated former U.S. Rep. Patrick Murphy, 53 percent to 47 percent with 98 percent of the vote counted.
Also Tuesday, presumptive GOP presidential nominee Mitt Romney won Pennsylvania along with four other states. The results, though, do not necessarily guarantee the former Massachusetts governor the support of all of the state's delegates to the national convention in Tampa, Fla., in August. Under state party rules, the 72 delegates are free to support the candidate of their choice at the convention.
In the U.S. Senate primaries, Democrat Bob Casey of Scranton easily beat a little-known challenger in his bid for a second six-year term. His Republican challenger will be wealthy former coal company owner Tom Smith of Armstrong County, who largely self-financed his victory in a bitter, five-way race in which he trounced the candidate endorsed by Gov. Tom Corbett and the state GOP.
Fewer than one in three Republicans and one in five Democrats voted in top-of-the-ticket races, as the western region was still dealing with the remnants of a winter storm.
In balloting in the state's newly redrawn congressional districts, voters passed over two veteran Democratic U.S. House representatives, signaling the end of their careers in Washington.
Tenth-term U.S. Rep. Tim Holden, a centrist Democrat and the state's longest-serving member of Congress, lost the nomination to attorney Matt Cartwright in northeast Pennsylvania.
Across the state, U.S. Rep. Mark Critz beat fellow Democratic U.S. Rep. Jason Altmire after redistricting had drawn the two into the same district.
In another western Pennsylvania district, fifth-term GOP U.S. Rep. Tim Murphy, however, beat back challenger Evan Feinberg.
In the attorney general's race, Kane, 45, will square off in the November election against Cumberland County District Attorney David Freed, who was unopposed for the Republican nomination.
During the primary campaign, she touted her nearly 13 years of experience as a prosecutor while reminding voters that Murphy, a former Army lawyer who served in Iraq, had never tried a case in Pennsylvania courts.
Murphy, 38, stressed his five years in the U.S. Army Judge Advocate General Corps and asserted that he was the true Democrat in the race.
In a speech to his supporters after his defeat, Murphy struck a conciliatory tone and said he had called Kane to congratulate her.
"She ran a strong campaign and is a fierce competitor," he said. "In the end, no matter what our differences, Kathleen Kane and I know that Pennsylvania will be better off with a Democrat serving as attorney general."
In another row-office contest, for the Republican nod for state auditor general, state Rep. John Maher of Allegheny County defeated banking lobbyist Frank Pinto.
In the state House of Representatives, five incumbent members lost primaries, including three with decades of legislative experience. Democrats won five of six special elections held to fill vacancies, a one-seat pickup that left Republicans still in firm control, 111-92.
Among the legislative primary winners was former state Rep. Bill DeWeese. He was unopposed and received 3,054 votes - more than the combined total of the two Republicans in the GOP primary - even though he was sentenced to prison Tuesday on a corruption conviction.
The primary represented the first test for the state's new voter identification mandate, although the photo IDs will not be required until November.
Secretary of State Carol Aichele visited some polling places in Philadelphia and concluded the new law seemed to be working well.
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Associated Press reporters Marc Levy in Harrisburg and Genaro Armas in State College contributed to this report.
